This is $300,000 ÷ 1.09. This is not a reasonable answer to the question. This is a discounted note, which means that the interest is calculated on the gross amount of the note, and the interest is subtracted from the gross amount to find the amount the borrower actually receives. However, the borrower must pay back the entire gross amount, including the interest. If the net proceeds of the note needs to be $300,000 and interest is subtracted from the face amount to calculate the net proceeds, the face amount of the note must be greater than the $300,000 net proceeds needed. This amount is less than the $300,000 net proceeds needed.
This is $300,000 ÷ .917, the present value of $1 factor for 9% for one year. The present value of a given amount (here unknown) is the amount an investor could invest today at the given interest rate (here 9%) if the investor had it, and with the interest added, it would grow to the given amount in the given amount of time (here one year). That is not the situation here. This is a discounted note, which means that the interest is calculated on the gross amount of the note, and the interest is subtracted from the gross amount to find the amount the borrower actually receives. However, the borrower must pay back the entire gross amount, including the interest. The usual type of interest calculation will not work in this situation, because of the fact that the interest amount paid by the borrower is not based on the amount the borrower receives. In fact, the effective rate of interest on a loan like this is higher than its stated rate because the borrower has to pay interest on a principal amount that is greater than the amount the borrower receives. If the effective interest rate were known, dividing $300,000 by the factor for that interest rate would result in the correct answer. But the effective interest rate on the loan cannot be calculated until the correct answer to this question has been calculated and the interest amount is known. So dividing $300,000 by the factor for the effective interest rate cannot be used to find the answer to this problem, either.
This is a discounted note, which means that the interest is calculated on the gross amount of the note, and the interest is subtracted from the gross amount to find the amount the borrower actually receives. However, the borrower must pay back the entire gross amount, including the interest. This is $300,000 × 1.09. Multiplying by 1.09 effectively calculates 9% of $300,000 and adds that to $300,000. However, $300,000 is what the net proceeds of the loan needs to be after the discounted interest has been subtracted from the face amount of the note. The bank will calculate the 9% discounted interest on the face amount (the gross amount) of the note instead.
This is a discounted note, which means that the interest is calculated on the gross amount of the note, and the interest is subtracted from the gross amount to find the amount the borrower actually receives. However, the borrower must pay back the entire gross amount, including the interest. If the discount rate is 9%, 9% of the gross loan amount will be subtracted from the face amount of the note to determine the amount the borrower will receive. Gates needs $300,000. Therefore, the formula we will use to find the face amount of the note will be: X ? .09X = $300,000 Where X = the face amount of the note Simplifying that equation, we get: .91X = $300,000 Solving for X, we get X = $329,670; and that is the amount that Gates will need to borrow in order to receive a net amount of $300,000 from the loan disbursement. To prove that answer: $329,670 × .09 = $29,670. $329,670 ? $29,670 = $300,000, the net disbursement the borrower needs to receive.
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